关于循环子半群的结构与数量问题及拟环的特征与结构

彻底解决了所有循环半群及其子群的结构和数量问题,并讨论了拟群分解问题,同时,对群论基本定理作了部分推广,并给出了定理的另一部分不可推广的反例,最后,建立了一类特殊环－拟环。     

The extension and completion of the universal measure and the dual of the space of measures

Every vector measure μ factors uniquely by μ = $\text{}\text{?}$gm ° χ where χ is a universal measure and $\text{}\text{?}$gm is a linear map continuous on simple functions in the strict topology. The completion of χ describes the dual of the space of measures by uniform closure based on χ-measurable sets and also as the completion of the simple functions in the strict topology.     

Reversal of the reinforcing effect of fillers and the relation between the flexibility of the macromolecules and the mechanical properties of filled polymers

The author describes various effects which he has detected involving the reversal of the reinforcing action of fillers in polymers in different subregions of the glassy state. It is suggested that these effects can be explained in terms of, among other things, the flexibility of the macromolecules. The concept of an optimal flexibility at which the maximum value of a given mechanical property can be realized is introduced. It is shown that it is possible, in principle, to reinforce a polymer in any subregion of the glassy state and even below T_b, as well as to obtain equal-strength, equal-modulus, equally reinforced, etc., composites containing different (large and small) amounts of fillers and plasticizers.     

Rigidity and stability of the Leibniz and the chain rule

We study rigidity and stability properties of the Leibniz and chain rule operator equations. We describe which non-degenerate operators V, T ₁, T ₂,A: C ^k (?) → C(?) satisfy equations of the generalized Leibniz and chain rule type for f, g ∈ C ^k (?), namely, V (f · g) = (T ₁ f) · g + f · (T ₂ g) for k = 1, V (f · g) = (T ₁ f) · g + f · (T ₂ g) + (Af) · (Ag) for k = 2, and V (f ○ g) = (T ₁ f) ○ g · (T ₂ g) for k = 1. Moreover, for multiplicative maps A, we consider a more general version of the first equation, V (f · g) = (T ₁ f) · (Ag) + (Af) · (T ₂ g) for k = 1. In all these cases, we completely determine all solutions. It turns out that, in any of the equations, the operators V, T ₁ and T ₂ must be essentially equal. We also consider perturbations of the chain and the Leibniz rule, T (f ○ g) = Tf ○ g · Tg + B(f ○ g, g) and T (f · g) = Tf · g + f · Tg + B(f, g), and show under suitable conditions on B in the first case that B = 0 and in the second case that the solution is a perturbation of the solution of the standard Leibniz rule equation.     

Convex decomposition of games and axiomatizations of the core and the D-core

This paper provides an axiomatic framework to compare the D-core (the set of undominated imputations) and the core of a cooperative game with transferable utility. Theorem 1 states that the D-core is the only solution satisfying projection consistency, reasonableness (from above), (*)-antimonotonicity, and modularity. Theorem 2 characterizes the core replacing (*)-antimonotonicity by antimonotonicity. Moreover, these axioms also characterize the core on the domain of convex games, totally balanced games, balanced games, and superadditive games.      

矩阵特征值、特征向量的确定

首先对由 A的特征值、特征向量求 A- 1 ,AT,A* ( A的伴随矩阵 )、P- 1 AP以及 A的多项式φ( A)的特征值和特征向量的结论作了个归纳 ;对相反的情形 ,我们给出了部分已有的结果 ,并通过四道例题着重讨论了如何由 φ( A)的特征值来求 A的特征值 .     

Adjoints and the image of the ball

A bounded operator between Hilbert spaces has an adjoint if and only if the image of the unit ball is located.

     

居民收入和消费预测的灰理论方法

阐述灰色模型GM(1,1)建立及检验的基本理论和方法.并依据2000年—2005年浙江农村居民人均纯收入和人均生活消费数据,利用GM(1,1)模型建模方法,对“十一五”期间浙江农民的纯收入和生活消费进行了预测.     

鱼咀及丁坝对长江口航道分流分沙的影响

利用水平二维水流、盐度、泥沙数学模型研究了长江口航道整治工程(一期)实施前后,航道的分水分沙特点,重点讨论了束水丁坝的长度、潜堤的方向对航道分流比、分沙比的影响．数值模拟结果表明,双导堤工程减少了航道的分沙量,这有利于维护航道的畅通,但同时也使航道的分流比减小．航道分流分沙比的改变可通过调整各水工建筑物的布置或尺寸来实现．与束水丁坝长度的影响相比,鱼咀工程潜堤方向的改变对航道分流分沙比的影响更大．     

Clinical evaluation of biotissues and synthetic prostheses in the reconstruction of the abdominal aorta and the arteries of the lower extremities

The long-term results of operations on the abdominal aorta and iliac arteries have been studied. It is shown that the use of arterial autografts after eversion endarterectomy does not have any particular advantages over the use of a prosthesis in relation to the prevention of postoperative thromboses. Eversion endarterectomy and autovenous shunting are the best methods for the plastic replacement of small and medium arteries.     

On the compactification of hyperconcave ends and the theorems of Siu-Yau and Nadel

We show that the ‘pseudoconcave holes’ of some naturally arising class of manifolds, called hyperconcave ends, can be filled in, including the case of complex dimension two. As a consequence we obtain a stronger version of the compactification theorem of Siu-Yau and extend Nadel’s theorems to dimension two. Mathematics Subject Classification (1991) 32J05, 32C22, 53C55     

函数与其反函数图像交点的个数及位置

讨论了函数与其反函数图像交点的个数及位置.同时举例说明我们的结果是精确的.     

Integrable couplings and Hamiltonian structures of the L-hierarchy and the T-hierarchy

An algebraic system is constructed from which establishes two isospectral problems. By solving the zero curvature equations, two resulting integrable couplings of the Li hierarchy and Tu hierarchy are obtained, respectively. By making use of the quadratic-form identity, the Hamiltonian structures of the above integrable couplings are generated, which are Liouville integrable.     

On the linear classification of even and odd permutation matrices and the complexity of computing the permanent

The problem of linear classification of the parity of permutation matrices is studied. This problem is related to the analysis of complexity of a class of algorithms designed for computing the permanent of a matrix that generalizes the Kasteleyn algorithm. Exponential lower bounds on the magnitude of the coefficients of the functional that classifies the even and odd permutation matrices in the case of the field of real numbers and similar linear lower bounds on the rank of the classifying map for the case of the field of characteristic 2 are obtained.     

On the Orthogonality of Frames and the Density and Connectivity of Wavelet Frames

We examine some recent results of Bownik on density and connectivity of the wavelet frames. We use orthogonality (strong disjointness) properties of frame and Bessel sequences, and also properties of Bessel multipliers (operators that map wavelet Bessel functions to wavelet Bessel functions). In addition we obtain an asymptotically tight approximation result for wavelet frames.     

On the approximation of positive operators and the behaviour of the spectra of the approximants

LetT be a positive linear operator on the Banach latticeE and let (S _n ) be a sequence of bounded linear operators onE which converge strongly toT. Our main results are concerned with the question under which additional assumptions onS _n andT the peripheral spectra (S _n ) ofS _n converge to the peripheral spectrum (T) ofT. We are able to treat even the more general case of discretely convergent sequences of operators.     

On the equivalence of the Heine-Borel and the Bolzano-Weierstrass theorems

The equivalence of the Heine-Borel theorem and the Bolzano-Weierstrass theorem is proved.     

Identification of parameters and the distribution of the minimum of the tri-variate normal

In this note, for tri-variate normal distributions, we consider the problem of the identification of parameters when only the distribution of the minimum is known.     

Analysis of the convergence of the minimal and the orthogonal residual methods

We consider two Krylov subspace methods for solving linear systems, which are the minimal residual method and the orthogonal residual method. These two methods are studied without referring to any particular implementations. By using the Petrov–Galerkin condition, we describe the residual norms of these two methods in terms of Krylov vectors, and the relationship between there two norms. We define the Ritz singular values, and prove that the convergence of these two methods is governed by the convergence of the Ritz singular values. AMS subject classification 65F10